Calibration weighting is a technique for adjusting randomization-based weights so that the estimator of a population total becomes unbiased under a linear prediction model. In the absence of nonresponse or frame errors, one set of calibration weights has been shown to be asymptotically optimal in some sense under Poisson sampling. Unfortunately, although it is desirable that each weight be at least one (so that the corresponding element “represents itself”), there is no guarantee that will be the case. We will see how to construct an asymptotically equivalent set of weights so that no weight is less than unity. One consequence is that it often will be a simple matter to construct a variance measure that simultaneously estimates the prediction variance and the randomization mean squared error of the estimator.
